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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 473165, 12 pages
http://dx.doi.org/10.1155/2015/473165
Research Article

Control for Nonlinear Systems with Time-Varying Delay Using Matrix-Based Quadratic Convex Approach

Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 30 November 2014; Revised 18 February 2015; Accepted 24 March 2015

Academic Editor: Qingling Zhang

Copyright © 2015 C. Emharuethai and P. Niamsup. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

control problem for nonlinear system with time-varying delay is considered by using a set of improved Lyapunov-Krasovskii functionals including some integral terms, and a matrix-based on quadratic convex, combined with Wirtinger's inequalities and some useful integral inequality. controller is designed via memoryless state feedback control and new sufficient conditions for the existence of the state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.